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Simplifying ln(6) + ln(2x + -1) = ln(3x + -2) Reorder the terms for easier multiplication: 6ln + ln(2x + -1) = ln(3x + -2) Reorder the terms: 6ln + ln(-1 + 2x) = ln(3x + -2) 6ln + (-1 * ln + 2x * ln) = ln(3x + -2) 6ln + (-1ln + 2lnx) = ln(3x + -2) Combine like terms: 6ln + -1ln = 5ln 5ln + 2lnx = ln(3x + -2) Reorder the terms: 5ln + 2lnx = ln(-2 + 3x) 5ln + 2lnx = (-2 * ln + 3x * ln) 5ln + 2lnx = (-2ln + 3lnx) Solving 5ln + 2lnx = -2ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. 5ln + 2ln + 2lnx = -2ln + 2ln + 3lnx Combine like terms: 5ln + 2ln = 7ln 7ln + 2lnx = -2ln + 2ln + 3lnx Combine like terms: -2ln + 2ln = 0 7ln + 2lnx = 0 + 3lnx 7ln + 2lnx = 3lnx Add '-3lnx' to each side of the equation. 7ln + 2lnx + -3lnx = 3lnx + -3lnx Combine like terms: 2lnx + -3lnx = -1lnx 7ln + -1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 7ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + -1x) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Add 'x' to each side of the equation. -1x + x = -7 + x Combine like terms: -1x + x = 0 0 = -7 + x Simplifying 0 = -7 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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